There was no historic rout this time for Arsenal and only a hint of the scintillating style that humiliated Everton 6-1 on their last visit to Goodison Park. And yet, paradoxically for Arsène Wenger, their latest triumph here brought more encouragement. On such results are championship challenges built.

The old stadium was as subdued as the teams for much of this contest but when Tim Cahill bundled home a Leighton Baines corner with a minute remaining, Everton finally stirred. When four minutes of added time went up, they sensed a repeat of September's remarkable fight-back from two goals down against Manchester United. But they, and perhaps the rest of the Premier League, had not reckoned with Arsenal's resilient spirit.

The much-maligned Lukasz Fabianski held firm, Johan Djourou and Alex Song threw themselves into every threat and when referee Howard Webb blew, the visitors found themselves bottom of the division's disciplinary table and, rather more importantly, two points behind Chelsea.

"I feel the performance has shown we have something that is not only quality football but spirit, and fighting spirit," said Wenger. "We have shown discipline, commitment, togetherness, desire, 100 per cent focus for 90 minutes and we got the three points. When you come here without that you don't get the three points. They are ingredients you need if you to fight for the championship like we want to do. At the moment Chelsea are at a different pace but we have to keep going." And this was before the result from Stamford Bridge made the journey home even more comfortable.

Neither Arsenal nor Everton delivered a great performance but the visitors' work without the ball, allied to the clinical touch in front of goal that David Moyes's team lack, set them apart. Their response to losing at home to Newcastle last weekend has been six points from Molineux and Goodison inside five days and a convincing riposte to criticism of their desire and maturity.

The breakthrough epitomised the performance of the two teams. Tim Howard saved well from the influential Samir Nasri but, as Everton hesitated on the loose ball, Arsenal seized the initiative. Andrei Arshavin turned the loose ball back to Bacary Sagna, the below-par Mikel Arteta stood watching, and the Arsenal right-back beat Howard at his near post with a venomous strike for only his second goal for the club in three years.

Arsenal extended their lead three minutes after the restart. Arteta was again at fault, losing possession after being played into trouble by Steven Pienaar, and the visitors broke with their customary precision. Denilson fed Cesc Fábregas, he exchanged passes with Marouane Chamakh, and then swept the ball low beyond Howard into the far corner.

After complaining this week about sitting on the bench Nicklas Bendtner failed to make the bench for Arsenal, but Wenger said there was nothing sinister in his omission and the player had suffered a slight injury setback.

"He had a little groin problem and I left him at home," said the Arsenal manager.

"I can't really say we deserved an awful lot," said Moyes. "I didn't think Arsenal were great on the day but I didn't think we were. Losing a goal just before half-time was crucial and then we gave away a terrible second goal. We never gave ourselves a chance after half time to get a head of steam and after that it was difficult."

Much of Goodison's ire was directed at the match official but Webb's erratic performance could not disguise Everton's familiar failings in front of goal and a lethargic start.

Webb again courted accusations of leniency when he rejected two controversial calls to show red to an Arsenal player.

Sebastien Squillaci tripped Louis Saha as the Everton striker broke clear of the Arsenal defence and seconds later Fábregas committed the kind of foul that understandably sends Wenger apoplectic when he caught Sylvian Distin after a clearance. Both received a yellow card, Saha's run away from goal saving Squillaci and Fábregas's trailing leg sparing the Arsenal captain, although, as Moyes said; "On both occasions I thought 'He's got a decision to make here'." Everton rallied belatedly but Fabianski saved well from Jermaine Beckford, Pienaar and Saha.